Statistic Homework Help

I would really appreciate it if anyone could help me with the following math problem from a homework assignment i have.

The principal at Jonesbury High School has claimed that the mean IQ of all students at the school is 125. The superintendent of schools in Jonesbury wants to test this claim. She checks the files of 36 Jonesbury High students at random, and finds that the mean IQ among these students is 124.8, with a standard deviation of .6. What is the smallest significance level at which the null hypothesis will be rejected? Hint: Calculate the p-value.

The principal at Jonesbury High School has claimed that the mean IQ of all students at the school is 125. The superintendent of schools in Jonesbury wants to test this claim. She checks the files of 36 Jonesbury High students at random, and finds that the mean IQ among these students is 124.8, with a standard deviation of .6. What is the smallest significance level at which the null hypothesis will be rejected? Hint: Calculate the p-value.

H_0 : u = 125
H_A : u ≠ 125

x = 125
u = 124.8
s = 0.6
n = 36

z = (x - u) / (s / sqrt(n))
= (125-124.8) / (0.6/6)
= 0.2 / 0.1 = 2

Thus, the two-tailed p-value = 0.02275026.

Now, if the p-value is lower than alpha, the null hypothesis is rejected. This means that alpha must be greater than (or equal to) 0.02275026 for the null hypothesis to be rejected. So, the smallest significance-level (alpha) such that H_0 gets rejected is about 0.02275026. Round this to as many digits as you wish.